Magnetism of Two Coupled Harmonic Oscillators

The thermodynamical properties of a system of two coupled harmonic oscillators in the presence of an uniform magnetic field B are investigated. Using an unitary transformation, we show that the system can be diagonalized in simple way and then obtain the energy spectrum solutions. These will be used to determine the thermodynamical potential in terms of different physical parameters like the coupling parameter \alpha. This allows us to give a generalization of already significant published work and obtain different results, those could be used to discuss the magnetism of the system. Different limiting cases, in terms of \alpha and B, have been discussed. In fact, quantum corrections to the Landau diamagnetism and orbital paramagnetism are found.Comment: 25 page

Accessing the strong interaction between Λ baryons and charged kaons with the femtoscopy technique at the LHC

The interaction between Λ baryons and kaons/antikaons is a crucial ingredient for the strangeness S=0 and S=-2 sector of the meson–baryon interaction at low energies. In particular, the Lambda-Kbar might help in understanding the origin of states such as the Csi(1620), whose nature and properties are still under debate. Experimental data on Lambda-K and Lambda-Kbar systems are scarce, leading to large uncertainties and tension between the available theoretical predictions constrained by such data. In this Letter we present the measurements of Λ–KK− and Λ–KK+ correlations obtained in the high-multiplicity triggered data sample in pp collisions at sqrt(s) = 13 TeV recorded by ALICE at the LHC. The correlation function for both pairs is modeled using the Lednický–Lyuboshits analytical formula and the corresponding scattering parameters are extracted. The Λ–KK+ correlations show the presence of several structures at relative momenta k* above 200 MeV/c, compatible with the Ω baryon, the , and resonances decaying into Λ–K− pairs. The low k* region in the Λ–KK+ also exhibits the presence of the state, expected to strongly couple to the measured pair. The presented data allow to access the ΛK+ and ΛK− strong interaction with an unprecedented precision and deliver the first experimental observation of the decaying into ΛK−

Measurement of electrons from beauty-hadron decays in pp and Pb-Pb collisions at sNN=5.02 TeV

The production of electrons from beauty-hadron decays was measured at midrapidity in proton-proton (pp) and central Pb-Pb collisions at center-of-mass energy per nucleon-nucleon pair √s NN = 5.02 TeV, using the ALICE detector at the LHC. The cross section measured in pp collisions in the transverse momentum interval 2 < pT < 8 GeV/c was compared with models based on perturbative quantum chromodynamics calculations. The yield in the 10% most central Pb-Pb collisions, measured in the interval 2 < pT < 26 GeV/c, was used to compute the nuclear modification factor RAA, extrapolating the pp reference cross section to pT larger than 8 GeV/c. The measured R AA shows significant suppression of the yield of electrons from beauty-hadron decays at high pT and does not show a significant dependence above 8 GeV/c within uncertainties. The results are de- scribed by several theoretical models based on different implementations of the interaction of heavy quarks with a quark-gluon plasma, which predict a smaller energy loss for beauty quarks compared to light and charm quark

Measurement of the Lifetime and Λ Separation Energy of _{Λ}^{3}H

The most precise measurements to date of the _{Λ}^{3}H lifetime τ and Λ separation energy B_{Λ} are obtained using the data sample of Pb-Pb collisions at sqrt[s_{NN}]=5.02  TeV collected by ALICE at the LHC. The _{Λ}^{3}H is reconstructed via its charged two-body mesonic decay channel (_{Λ}^{3}H→^{3}He+π^{-} and the charge-conjugate process). The measured values τ=[253±11(stat)±6(syst)]  ps and B_{Λ}=[102±63(stat)±67(syst)]  keV are compatible with predictions from effective field theories and confirm that the _{Λ}^{3}H structure is consistent with a weakly bound system

First measurement of Λc+ production down to pT=0 in pp and p-Pb collisions at sNN=5.02 TeV

The production of prompt Lambda+c baryons has been measured at midrapidity in the transverse momentum interval 0 < pT < 1 GeV/c for the first time, in pp and p–Pb collisions at a center-of-mass energy per nucleon-nucleon collision √s NN = 5.02 TeV. The measurement was performed in the decay channel Lambda+c → pK0S by applying new decay reconstruction techniques using a Kalman-Filter vertexing algorithm and adopting a machine-learning approach for the candidate selection. The pT -integrated Lambda+c production cross sections in both collision systems were determined and used along with the measured yields in Pb–Pb collisions to compute the pT -integrated nuclear modification factors R pPb and R AA of Lambda+c baryons, which are compared to model calculations that consider nuclear modification of the parton distribution functions. The Lambda+c /D0 baryon-to-meson yield ratio is reported for pp and p–Pb collisions. Comparisons with models that include modified hadronization processes are presented, and the implications of the results on the understanding of charm hadronization in hadronic collisions are discussed. A significant (3.7σ ) modification of the mean transverse momentum of Lambda+c baryons is seen in p–Pb collisions with respect to pp collisions, while the pT -integrated Lambda+c /D0 yield ratio was found to be consistent between the two collision systems within the uncertainties

Investigation of K+K- interactions via femtoscopy in Pb-Pb collisions at sNN =2.76 TeV at the CERN Large Hadron Collider

Femtoscopic correlations of nonidentical charged kaons (K+K-) are studied in Pb-Pb collisions at a center-of-mass energy per nucleon-nucleon collision sNN=2.76 TeV by ALICE at the CERN Large Hadron Collider. One-dimensional K+K- correlation functions are analyzed in three centrality classes and eight intervals of particle-pair transverse momentum. The Lednický and Luboshitz interaction model used in the K+K- analysis includes the final-state Coulomb interactions between kaons and the final-state interaction through a0(980) and f0(980) resonances. The mass of f0(980) and coupling were extracted from the fit to K+K- correlation functions using the femtoscopic technique. The measured mass and width of the f0(980) resonance are consistent with other published measurements. The height of the φ(1020) meson peak present in the K+K- correlation function rapidly decreases with increasing source radius, qualitatively in agreement with an inverse volume dependence. A phenomenological fit to this trend suggests that the φ(1020) meson yield is dominated by particles produced directly from the hadronization of the system. The small fraction subsequently produced by final-state interactions could not be precisely quantified with data presented in this paper and will be assessed in future work

Measurement of the non-prompt D-meson fraction as a function of multiplicity in proton-proton collisions at s \sqrt{s} = 13 TeV

The fractions of non-prompt (i.e. originating from beauty-hadron decays) D0 and D+ mesons with respect to the inclusive yield are measured as a function of the charged-particle multiplicity in proton-proton collisions at a centre-of-mass energy of √s = 13 TeV with the ALICE detector at the LHC. The results are reported in intervals of transverse momentum (pT) and integrated in the range 1 < pT < 24 GeV/c. The fraction of non-prompt D0 and D+ mesons is found to increase slightly as a function of pT in all the measured multiplicity intervals, while no significant dependence on the charged- particle multiplicity is observed. In order to investigate the production and hadronisation mechanisms of charm and beauty quarks, the results are compared to PYTHIA 8 as well as EPOS 3 and EPOS 4 Monte Carlo simulations, and to calculations based on the colour glass condensate including three-pomeron fusion

Enhanced Deuteron Coalescence Probability in Jets

: The transverse-momentum (p_{T}) spectra and coalescence parameters B_{2} of (anti)deuterons are measured in p-p collisions at sqrt[s]=13  TeV for the first time in and out of jets. In this measurement, the direction of the leading particle with the highest p_{T} in the event (p_{T}^{lead}>5  GeV/c) is used as an approximation for the jet axis. The event is consequently divided into three azimuthal regions, and the jet signal is obtained as the difference between the toward region, that contains jet fragmentation products in addition to the underlying event (UE), and the transverse region, which is dominated by the UE. The coalescence parameter in the jet is found to be approximately a factor of 10 larger than that in the underlying event. This experimental observation is consistent with the coalescence picture and can be attributed to the smaller average phase-space distance between nucleons in the jet cone as compared with the underlying event. The results presented in this Letter are compared to predictions from a simple nucleon coalescence model, where the phase-space distributions of nucleons are generated using pythia8 with the Monash 2013 tuning, and to predictions from a deuteron production model based on ordinary nuclear reactions with parametrized energy-dependent cross sections tuned on data. The latter model is implemented in pythia8.3. Both models reproduce the observed large difference between in-jet and out-of-jet coalescence parameters, although the almost flat trend of the B_{2}^{Jet} is not reproduced by the models, which instead give a decreasing trend

First measurement of prompt and non-prompt D⁎+ vector meson spin alignment in pp collisions at s=13 TeV

This letter reports the first measurement of spin alignment, with respect to the helicity axis, for D*+ vector mesons and their charge conjugates from charm-quark hadronisation (prompt) and from beauty-meson decays (non-prompt) in hadron collisions. The measurements were performed at midrapidity (|y| D0 (-> K- pi+) pi+ decay products, in the D*+ rest frame, with respect to the D*+ momentum direction in the pp centre of mass frame. The rho_00 value for prompt D*+ mesons is consistent with 1/3, which implies no spin alignment. However, for non-prompt D*+ mesons an evidence of rho_00 larger than 1/3 is found. The measured value of the spin density element is in the interval, which is consistent with a Pythia 8 Monte Carlo simulation coupled with the EvtGen package, which implements the helicity conservation in the decay of D*+ meson from beauty mesons. In non-central heavy-ion collisions, the spin of the D*+ mesons may be globally aligned with the direction of the initial angular momentum and magnetic field. Based on the results for pp collisions reported in this letter it is shown that alignment of non-prompt D*+ mesons due to the helicity conservation coupled to the collective anisotropic expansion may mimic the signal of global spin alignment in heavy-ion collisions

Production of pions, kaons, and protons as a function of the relative transverse activity classifier in pp collisions at s \sqrt{s} = 13 TeV

Abstract: The production of π±, K±, and ( p )p is measured in pp collisions at √s = 13 TeV in different topological regions of the events. Particle transverse momentum (pT) spectra are measured in the “toward”, “transverse”, and “away” angular regions defined with respect to the direction of the leading particle in the event. While the toward and away regions contain the fragmentation products of the near-side and away-side jets, respectively, the transverse region is dominated by particles from the Underlying Event (UE). The relative transverse activity classifier, RT = NT/〈NT〉, is used to group events according to their UE activity, where NT is the measured charged-particle multiplicity per event in the transverse region and 〈NT〉 is the mean value over all the analysed events. The first measurements of identified particle pT spectra as a function of RT in the three topological regions are reported. It is found that the yield of high transverse momentum particles relative to the RT-integrated measurement decreases with increasing RT in both the toward and the away regions, indicating that the softer UE dominates particle production as RT increases and validating that RT can be used to control the magnitude of the UE. Conversely, the spectral shapes in the transverse region harden significantly with increasing RT. This hardening follows a mass ordering, being more significant for heavier particles. Finally, it is observed that the pT-differential particle ratios (p + p )/(π+ + π−) and (K+ + K−)/(π+ + π−) in the low UE limit (RT → 0) approach expectations from Monte Carlo generators such as PYTHIA 8 with Monash 2013 tune and EPOS LHC, where the jet-fragmentation models have been tuned to reproduce e+e− results